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Fields Analysis Working Group

The Fields Analysis Working Group (FAWG) seminars are a working group seminar and brown bag lunch devoted to nonlinear dynamics and the calculus of variations meeting once a week.. Interested persons are welcome to attend and to propose talks to the organizers Larry Guth, Robert McCann and James Colliander.

Seminars will be held on Thursdays at 12 noon in Room 210 at the Fields Institute unless stated otherwise.

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Details

Conductivity imaging from one interior measurement in the presence of perfectly conducting and insulating inclusions

by
Amir Moradifam
(www)
|
University of Toronto
Time: 12:10 (Thursday, Oct. 20, 2011)Location: FI210, Fields Institute, 222 College St.Abstract:
We consider the problem of recovering an isotropic conductivity outside some perfectly conducting or insulating inclusions from the interior measurement of the magnitude of one current density field $|J|$. We prove that the conductivity outside the inclusions, and the shape and position of the perfectly conducting and insulating inclusions are uniquely determined (except in an exceptional case) by the magnitude of the current generated by imposing a given boundary voltage. We have found an extension of the notion of admissibility to the case of possible presence of perfectly conducting and insulating inclusions. This makes it possible to extend the results on uniqueness of the minimizers of the least gradient problem $F(u)=\int_{\Omega} a|\nabla u|$ with $u|_{\partial \Omega}=f$ to cases where u has flat regions (is constant on open sets). This is a joint work with Adrian Nachman and Alexandru Tamasam.